Evaluate the integral 25 6)"dx - by making the substitution u = x -6. + C NOTE: Your answer should be in terms of x and not u.

Q: 4 dr. 162? — 16х +13 Use the Table of Integrals in the back of your textbook to evaluate Perform the…

A: Indefinite Integration

Q: Solve the integral by trigonometric substitution: (z+3)* dz. (40 – 6z – 22) - -

A: Given: To solve the given integral by trigonometric solution: ∫(z+3)540-6z-z232dz

Q: Evaluate the integral. * T/3 3 sec 0 tan 0 de In/4

A: Given that the integral is ∫π4π33secθtanθdθ. It is required to evaluate the given integral…

Q: 2. Use Cauchy's Integral formula, Evaluate the following sin42 IZ1= 3. (Z-4)3

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Evaluate the integral. 37/4 3 sec e tan e de -7/4

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Q: Use symmetry to evaluate the following integral. 6 | (36 -x) dx -6 | (36-x) dx: -6

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Q: (a) Evaluate the integral | 16х -dx by using substitution. 8x +2 (b) Evaluate the integral using by…

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Q: To evaluate the integral 1. 7 64 + x² -dx,

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Q: 2 B. Evaluate | (2- x) dx by interpreting the integral in terms of area. -1

A: Topic = Integration

Q: 9. Find the integral, using u substituti x-(1-3x²)*dx a.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Find the complete integral xp+3yq D2 (z - xq). 2 2 the

A: Consider the given equation: The objective is to find the complete integral of given equation.

Q: Evaluate the integral (8 – „2),"| I dx, 4. by making the appropriate substitution: u = = xp |-…

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Q: 14. Verify that f cotx dx = In(sin x) +C. (Do not try to solve the integral from scratch.) %3D

A: Given: verify that ∫cotxdx=lnsinx+c For verifying given integral, we integrate given integral

Q: Evaluate the integral. "T/3 8 sec 0 tan 8 de IT/4

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Q: Use properties of the integral and the formulas in the summary to calculate the integrals.

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Q: Evaluate the integral. 5, sec 3x tan 3x dx sec $3x tan 3x dx =D

A: To evaluate: I=∫sec53x tan 3x dx=∫sec43x sec 3x tan 3x dx

Q: Compute the approximation  of the integral -4 to 4 e^(-x^2) using right endpoints with 4 rectangles;…

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Q: Evaluate the integral (ez – 107) dr

A: Solve the following integral

Q: Use thě substitution a = 7 tan(0) to evaluate the indefinite integral 40dx x²Væ² + 49 +C

A: Substitute x=7tanθ After differentiating, dx=7sec2θdθ

Q: Evaluate the integral. *5 1³ v +² + 25 dx

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Q: Find the indefinite integral

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Q: Evaluate the indefinite integral: (8e" + 5 sec? u) du =| + C.

A: We use integration of eu=eu and integration of sec2u= tanu .

Q: u= 4-xneduce the ntegral to standand ferm Sonm dx 4-x)=

A: ∫x64-x72dx In this problem we need to reduce the given equation into standard form and solve the…

Q: Evaluate the integral. -2. 3 17 secx tanx dx

A:

Q: 5) Evaluate the integrals using appropriate substitutions a) sec 2x tan 2x dx b) 2x+1

A: Given that, a) ∫sec32x tan 2x dx b) ∫x2x+1dx For evaluating those indefinite integrals,  we need to…

Q: Evaluate the integral (2х — 8)dx х2 — 6х + 18

A: We know that integration power rule is - Integration of xn is xn+1/n+1+ C  Here C is integration…

Q: 36 Use substitution to find the indefinite integral dx. (6x - 7) 36 dx = 7 (6x - 7)'

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Q: Evaluate the Indefinite Integral 6x! -dx За? + 14

A: To evaluate the given indefinite integral- ∫6x3x2+14dx Here we will use the following integration…

Q: 1- 3 sin (x) dx. 2 cos2 (x)

A: Computer the Integral

Q: 8. Evaluate the integral by using trigonometric substitution 2 dx V4x – x2

A: We have to find the indefinite integral.

Q: Consider the indefinite integral 7x4 dx 7x5 – 9 - (a) The most appropriate substitution

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Q: Evaluate the integral.

A: Consider the following integral:…

Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

Q: Q/ comput the integral following in more ways than one. dx JI+ tan(x)

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Q: Use a double integral to find the area of the shaded region. n/2 10 r = 8 cos 20 5 - 10 -5 5 10 -5…

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Q: de 2/2 V5 9 18

A: Solution: Here let I=∫dxx29-x2 Substitute: x=3sinu u=sin-1x3 and dx=3cosudu Thus,…

Q: Compute the given improper integral. Enter the exact value of the answer. 1 /x² 400 29 So - dx =

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Q: Evaluate the indefinite integral: (3e" + 6 sec? u) du: |+ C.

A: As per guide line we have

Q: 4. Prove using the results concerning iterated integrals that In 5 dx = 4 sin? x

A: Given:-                 To prove the result concerning iterated integrals that…

Q: 4 -dx is divergent. 1-2х (b) Show that the improper integral

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Q: Use u-substitution to evaluate the integral: 7x^2 square root2x^3-1 dx

A: Given,          ∫7x22x3-1dx

Q: | У49х2 + 1225 dx

A: We have to find

Q: Evaluate the integrals using trigonometric substitution dz 2² √2²-4

A: Find the inegrals by Trignormeric substitution

Q: Evaluate the integral: =°/1+ 64z*dz

A:

Q: Use the substitution formula to evaluate the integral. the integral from 0 to pie/2…

A: To  Determine:Use the substitution formula to evaluate the integral. Given: we have an integral…

Q: Evaluate the definite integral. 5 4u [(-*--*--* du (u + 3)² 4 5 1 ((---)-D 4u du (u+3)²2 4 (Type an…

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Q: 10. f3, (x²-1) dx

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Q: Solve the integral by two grid in the y-direction and four grid in the x-direction with Trapezoidal…

A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By Trapezoidal rule,…